an:05197001
Zbl 1122.81038
De Pace, A.; Molinari, A.; Weidenm??ller, H. A.
Interaction of regular and chaotic states
EN
Ann. Phys. 322, No. 10, 2446-2468 (2007).
00211979
2007
j
81Q50 15B52
Chaos; random-matrix theory; doorway state; spreading width
Summary: Modelling the chaotic states in terms of the Gaussian Orthogonal Ensemble of random matrices (GOE), we investigate the interaction of the GOE with regular bound states. The eigenvalues of the latter may or may not be embedded in the GOE spectrum. We derive a generalized form of the Pastur equation for the average Green's function. We use that equation to study the average and the variance of the shift of the regular states, their spreading width, and the deformation of the GOE spectrum non-perturbatively. We compare our results with various perturbative approaches.